A note on damped wave equations with a nonlinear dissipation in non-cylindrical domains

TL;DR

This paper investigates the long-term behavior of damped wave equations with nonlinear dissipation in non-cylindrical domains, relaxing previous restrictions on the nonlinear term coefficients and domain conditions.

Contribution

It extends existing results by allowing more general nonlinear coefficients and less restrictive domain conditions for the wave equation with nonlinear damping.

Findings

Relaxed conditions on nonlinear coefficient (t) for wave equations.

Established decay properties of solutions in non-cylindrical domains.

Generalized the class of domains where damping effects are analyzed.

Abstract

In this paper, we study the large time behavior of a class of wave equation with a nonlinear dissipation in non-cylindrical domains. The result we obtained here relaxes the conditions for the nonlinear term coefficients (in precise, that is $\beta(t)|u|^\rho u$) in \cite{alb} and \cite{ha} (which require $\beta(t)$ to be a constant or $\beta(t)$ to be decreasing with time $t$) and has less restriction for the defined regions.